(2x-5)(3x-1)=-7

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Solution for (2x-5)(3x-1)=-7 equation: 


Simplifying
(2x + -5)(3x + -1) = -7

Reorder the terms:
(-5 + 2x)(3x + -1) = -7

Reorder the terms:
(-5 + 2x)(-1 + 3x) = -7

Multiply (-5 + 2x) * (-1 + 3x)
(-5(-1 + 3x) + 2x * (-1 + 3x)) = -7
((-1 * -5 + 3x * -5) + 2x * (-1 + 3x)) = -7
((5 + -15x) + 2x * (-1 + 3x)) = -7
(5 + -15x + (-1 * 2x + 3x * 2x)) = -7
(5 + -15x + (-2x + 6x2)) = -7

Combine like terms: -15x + -2x = -17x
(5 + -17x + 6x2) = -7

Solving
5 + -17x + 6x2 = -7

Solving for variable 'x'.

Reorder the terms:
5 + 7 + -17x + 6x2 = -7 + 7

Combine like terms: 5 + 7 = 12
12 + -17x + 6x2 = -7 + 7

Combine like terms: -7 + 7 = 0
12 + -17x + 6x2 = 0

Factor a trinomial.
(4 + -3x)(3 + -2x) = 0


Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {1.333333333, 1.5}

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